For context, an implicit character is a control sequence that has been \let to a character. For example, both plain TeX and LaTeX use \let\bgroup{ \let\egroup} making \bgroup and \egroup into implicit braces.

In some places, TeX accepts either, in other places, it does not. For example, implicit braces cannot be used to collect tokens for undelimited macro arguments, nor can they be used to delimit the replacement text of a macro assignment.

Implicit braces can be used

to form groups: \bgroup...\egroup;

to construct boxes: \hbox, \vbox, and \vtop;

to create vertical material with \insert or \vadjust;

for alignment material with \halign, \valign, and \noalign; and

to create a new math atom.

Implicit left braces—which must be matched with literal characters with category code 2 (e.g., }2)—can be used

to assign to token variables;

with \hyphenation and \patterns;

to change case with \uppercase and \lowercase;

to write messages using \message or \errmessage;

to write files using \write;

to construct a \special;

for \mark;

for \discretionary; and

for a four-way \mathchoice.

I tried to be thorough, but TeX is extremely complicated. Are there any other places where an implicit brace can be used instead of an explicit one?

As far as I can make out, these are all the cases in TeX82. The new extended typesetting engines will have longer primitive lists for explicit right braces, but the same basic rule about closing a token list will apply.